Chapter 16- Interference and Diffraction 16.1 Interference
Interference can occur between waves of the same wavelength or monochromatic light. If crests or troughs interfere or overlap with each other, there phase displacement is 0 degrees and the waves are said to be in phase. If a crest and trough interfere with each other they have a phase displacement of 180 degrees, the waves are said to be out of phase. If light from a single source is passed through two narrow parallel slits they will serves as coherent sources and will produce an injterference pattern with a bright fringe where constructive interference occurs and dark ones in between.
How waves interact
How waves interfere, from book
The fringes are numbered with an order number, the center one being zero and the others are numbered outward. The dark fringes are also numbered starting with zero, but there are two zeroeth-order dark fringes. Dark fringes are referred to as maximums while light fringes are referred to as maximums.
For two slits separated by a distance d, the mth order maximum is located at some angle from a normal line drawn betweeen the slits, that angle also depends on the wavelength.
The equation for this relationship is:
In this equation m equals 0 and all positive and negative integers as the fringes will go on forever.
Dark fringes can be found using the same equation except adding ½ for the order number. This makes the equation:
How the equation works, from book
If the difference in distances is an integral multiple of the wavelength then a bright fringe will be seen, if the difference is half a wave length then you will see a dark fringe.
With white light the interference pattern will break up the colors of the spectrum and a bright fringe will consist of each color being seen.
16.2 Diffraction
Huygens principle states that each point on a wave front is the source of a new wavelet. Slits will act as the source of a new wave. Light deviates from a straight-line path and enters the area that would normally be in shadow (diffraction) and produces a diffraction pattern when the wavelets interfere with each other. This can occur when light passes through a slit or when it passes by the edge of an object.
Wavelets being emitted from a single source, physics book
White light diffraction, from book
When light passes through a diffraction grating each adjacent pair of grooves in the grating will behave like two slits. The same equation will work to find the location of the fringes.
Diffraction is used to determine the resolving power of an optical instrument. The resolving power is the instrument's ability to distinguish two objects that appear to be close to each other as seperate images. 16.3 Lasers
In a normal light source, rays of light are emitted randomly. In a laser, the light all has the same wavelength and is emitted in phase as coherent light.
Lasers take advantage of properties of the energy levels of an electron in certain atoms. They do this by pumping energy into the atom bringing the electrons down to an excited state, which then spontaneously decay to a metastable state. Many electrons build up at the metastable state and then a photon knocks them all down to a ground state. Thus, the waves all have the same wavelength and are emitted in phase. Since they are emitted in phases they are called coherent light. Lasers are much more intense because of the coherency of the light.
Thin-Film Interference
When light bounces off a soap bubble it is reflected off the outside and inside surfaces. Thus depending on the thickness of the bubble, the light reflecting off the inner and outer surfaces will be in or out of phase with light on the other surface. If the thickness is ¼ the wavelength then there will be constructive interference. If it is ½ the wavelength then there will be destructive interference. The patteren will continue with each quarter wavelength added to the thickness. Since the thickness is not uniform across the bubble, horizontal bands will be observed. If the bubbles are lit with one color then the pattern will be light and dark bands. However if it is lit with white light a rainbow will be observed. Thin oil films work this way as well.
Anti-reflection lenses work the same way, however, a very thin coating of magnesium flouride is deposited on the surface of a glass lens to provide destructive interference for most wavelengths of visible light. The main difference is ¼ the wavelength will create destructive interference while contructive interference will occur at ½ the wavelength.
Review Problems
1. Light falls on a double slit seperated by 2.02 x 10^-6 m and the first bright fringe is seen at an angle of 16.5° relative to the central maximum. Find the wavelength of the light.
2. A diffraction grating is calibrated by using the 546.1 nm line of mercury vapor. The first order maximum is found at an angle of 21.2°. Calculate the number of lines per meter on this grating.
3. A double-slit experiment is performed with red light and then again with blue light. In what ways do the two interference patterns differ?
Answers
1. 5.74 x 10^-7 m, plug into the equation.
2. 6.62 x 10^5 lines/m, plug into the equation sovling for d and don't forget to turn nanometers into meters. Then invert the answer.
3. The angles are different for the maximums and minimums.
Citations
Serway, and Faughn. Holt Physics. New York: Holt Rinehart & Winston, 2002.
16.1 Interference
Interference can occur between waves of the same wavelength or monochromatic light. If crests or troughs interfere or overlap with each other, there phase displacement is 0 degrees and the waves are said to be in phase. If a crest and trough interfere with each other they have a phase displacement of 180 degrees, the waves are said to be out of phase. If light from a single source is passed through two narrow parallel slits they will serves as coherent sources and will produce an injterference pattern with a bright fringe where constructive interference occurs and dark ones in between.
The fringes are numbered with an order number, the center one being zero and the others are numbered outward. The dark fringes are also numbered starting with zero, but there are two zeroeth-order dark fringes. Dark fringes are referred to as maximums while light fringes are referred to as maximums.
For two slits separated by a distance d, the mth order maximum is located at some angle from a normal line drawn betweeen the slits, that angle also depends on the wavelength.
The equation for this relationship is:
In this equation m equals 0 and all positive and negative integers as the fringes will go on forever.
Dark fringes can be found using the same equation except adding ½ for the order number. This makes the equation:
If the difference in distances is an integral multiple of the wavelength then a bright fringe will be seen, if the difference is half a wave length then you will see a dark fringe.
With white light the interference pattern will break up the colors of the spectrum and a bright fringe will consist of each color being seen.
16.2 Diffraction
Huygens principle states that each point on a wave front is the source of a new wavelet. Slits will act as the source of a new wave. Light deviates from a straight-line path and enters the area that would normally be in shadow (diffraction) and produces a diffraction pattern when the wavelets interfere with each other. This can occur when light passes through a slit or when it passes by the edge of an object.
When light passes through a diffraction grating each adjacent pair of grooves in the grating will behave like two slits. The same equation will work to find the location of the fringes.
Diffraction is used to determine the resolving power of an optical instrument. The resolving power is the instrument's ability to distinguish two objects that appear to be close to each other as seperate images.
16.3 Lasers
In a normal light source, rays of light are emitted randomly. In a laser, the light all has the same wavelength and is emitted in phase as coherent light.
Lasers take advantage of properties of the energy levels of an electron in certain atoms. They do this by pumping energy into the atom bringing the electrons down to an excited state, which then spontaneously decay to a metastable state. Many electrons build up at the metastable state and then a photon knocks them all down to a ground state. Thus, the waves all have the same wavelength and are emitted in phase. Since they are emitted in phases they are called coherent light. Lasers are much more intense because of the coherency of the light.
Thin-Film Interference
When light bounces off a soap bubble it is reflected off the outside and inside surfaces. Thus depending on the thickness of the bubble, the light reflecting off the inner and outer surfaces will be in or out of phase with light on the other surface. If the thickness is ¼ the wavelength then there will be constructive interference. If it is ½ the wavelength then there will be destructive interference. The patteren will continue with each quarter wavelength added to the thickness. Since the thickness is not uniform across the bubble, horizontal bands will be observed. If the bubbles are lit with one color then the pattern will be light and dark bands. However if it is lit with white light a rainbow will be observed. Thin oil films work this way as well.
Anti-reflection lenses work the same way, however, a very thin coating of magnesium flouride is deposited on the surface of a glass lens to provide destructive interference for most wavelengths of visible light. The main difference is ¼ the wavelength will create destructive interference while contructive interference will occur at ½ the wavelength.
Review Problems
1. Light falls on a double slit seperated by 2.02 x 10^-6 m and the first bright fringe is seen at an angle of 16.5° relative to the central maximum. Find the wavelength of the light.
2. A diffraction grating is calibrated by using the 546.1 nm line of mercury vapor. The first order maximum is found at an angle of 21.2°. Calculate the number of lines per meter on this grating.
3. A double-slit experiment is performed with red light and then again with blue light. In what ways do the two interference patterns differ?
Answers
1. 5.74 x 10^-7 m, plug into the equation.
2. 6.62 x 10^5 lines/m, plug into the equation sovling for d and don't forget to turn nanometers into meters. Then invert the answer.
3. The angles are different for the maximums and minimums.
Citations
Serway, and Faughn. Holt Physics. New York: Holt Rinehart & Winston, 2002.